At some point after launch, usually just before or after separation from the last booster stage, spacecraft are often made to "spin" (about the axis of their trajectory)? See e.g this You Tube video. What is the reason for this spin?

just to add to the answers, every projectile is rotated to get additional stability eg. bullets; gun barrel have grooves in the shape of spirals to make the bullet spin..
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Vineet MenonDec 8 '12 at 12:49

Applying spin along an axis, usually the direction of travel, endows the craft with a degree of gyroscopic stability, enabling the craft to preserve consumables onboard as it makes navigation easier. SPin is also used in re-entry (like the beagle mars lander).

New Horizons, Pioneer 1 and 2, Voyager 1 and 2, as well as some sattellites all use a spin to gain gyroscopic stability.

Note that on liftoff some craft, such as the Space Shuttle, would spin a bit in order to point their UHF antennae at the ground station. You can see this in all the Shuttle launch videos as the shadows slide around a bit on the skin of the craft, and then stop.